A pullback theorem for locally-equiconnected spaces
type: Item
instance of: scholarly article
title: A pullback theorem for locally-equiconnected spaces
zbMATH Open document ID: 0595.55007
DOI: 10.1007/BF01168688
author: Philip R. Heath
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155139
review text: A space X is locally equiconnected (L.E.C.) if the inclusion of the diagonal \(\Delta\) X in \(X\times X\) is a cofibration. This paper contains the following result. Given any fibration \(p: E\to B\) and map \(f: X\to B\) where E, B and X are all LEC, then the pullback space \(X\varsubsetneq E=\{(x,e):\quad f(x)=p(e)\}\) is also LEC. This can be applied to construct for fibrations with path connected fibres, translation functions between fibres that are base point preserving [c.f. the author, Pac. J. Math. 117, 267-289 (1985; Zbl 0571.55002)].
Mathematics Subject Classification ID: 55P05
Mathematics Subject Classification ID: 54F99
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 3958225
zbMATH Keywords: locally equiconnected
zbMATH Keywords: cofibration
zbMATH Keywords: pullback
zbMATH Keywords: fibrations with path connected fibres
reviewed by: Timothy Porter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3958225